With the mass deploy of cameras, concern has risen about protecting a person's privacy as he goes about his daily life. Many of the cameras are installed to perform surveillance tasks that do not require the identity of a person. In the context of surveillance applications, we examine the trade-off better privacy and security. The trade-off is accomplished by looking at quantitative measures of privacy and surveillance performance. To provide privacy protection we examine the effect on surveillance performance of a parametric family of privacy function. A privacy function degrades images to make identification more difficult. By varying the parameter, Different levels of privacy protection are provided. We introduce the privacy operating characteristic (POC) to quantitatively show the resulting trade-off between privacy and security. From a POC, policy makers can select the appropriate operating point for a surveillance systems with regard to privacy.